The Luneberg lens. The simulation shown on the cover of this book is known as a Luneburg lens. The lens is defined by a permittivity = 0[2 - (r/R) 2], where R is the radius of the lens; the permittivity smoothly transitions to that of free space at its edge.
(a) Replicate the simulation on the cover for a 2D TM mode, at a frequency of 2 GHz with a lens of radius 1 m. Use a second-order Mur boundary on all edges. How well does the lens produce a plane wave as you vary the input frequency?
(b) Wrap the Luneberg lens with a total-field/scattered-field boundary, and run the simulation in reverse: excite the space with a plane at the left edge of the TF/SF boundary. Observe how well the Luneberg lens brings the incident plane wave to a focus. Compare its performance as you vary the input frequency.